Modeling targeted delivery of biomimetic polymer vesicle gene therapy to cancer

Lead Research Organisation: University of Strathclyde
Department Name: Mathematics and Statistics

Abstract

The aim of the project is to assess the feasibility of using nanoparticles to deliver chemotherapeutic drugs to cancer cells. The nanoparticles are synthetic and designed to encapsulate drugs and carry specific markers that target toxic effects efficiently to the tumour cells while protecting other tissues, and thus reducing systemic toxicity. The nanoparticles in question differ to other synthetic delivery devices in terms of their greater loading capacity, improved drug retention and better targeting efficiency. The biggest challenge in their design, however, is how to optimize their specificity of action.We will develop novel mathematical models to tackle this issue. We will use the latest modeling techniques to discover how infiltration, targeting and uptake of the nanoparticles are regulated by their size, mechanical, chemical and membrane properties. Data generated from in vitro lab experiments with the head and neck cancers will be used to inform the mathematical approach for parameterisation and validation. We will then extend the validated models to predict the therapeutic effect in tumours in vivo, focussing on tumours that have acquired a blood supply and developing a model framework which will help focus an in vivo experimental program before animal studies begin. This will permit the investigation of different experimental situations which are technically difficult and the collection of data limited, at a minimum of cost and use of animal models. These targeting issues are relevant to the delivery field in general so our model will also act as a framework for targeted delivery for other tumours as well as other pathologic conditions. The aims of the project are:(i) To develop novel mathematical models of ligand-receptor binding of nanoparticles to cancer cells to predict how targeting can be enhanced by modulating the numbers of ligands and 'stealth' particles on the nanoparticles.(ii) To use data generated from cancer cell culture experiments to parameterise and validate the mathematical models and assess infiltration and delivery patterns in cell populations andidentify conditions of non-specific and actual targeting.(iii) To develop spatio-temporal partial differential equation models to make predictions about nanoparticle stability and therapeutic efficiency given different particle sizes, fluidity and membrane properties and different loads and combinations of cytotoxic drugs with different hydrophobic-hydrophilic properties.(iv) To modify the mathematical models to determine whether acidic tumour conditions can trigger premature release of the vesicle contents.(v) To utilize the mathematical models to inform in vivo experimentation by generating testable hypotheses for determining therapeutic efficiency.

Planned Impact

One quarter of the population eventually develops cancer and the social (e.g. a reduced quality of life and life expectancy) and economic costs (e.g. medical costs and loss of earnings) are considerable. In monetary terms for the care of cancer patients, it is estimated that by 2012, we will see an above 200% increase to today's costs in caring for cancer patients (e.g. see Sikora, K., Cancer drugs - the economic challenge, Focus on Oncology, May 2008). Improvements in the treatment outcomes for some solid tumours have reached a plateau despite advances in surgery, chemo- and radio-therapy. Gene therapy offers the timely hope of a new and efficient tool for treating such diseases but safety concerns (including the possibility of inducing severe systemic toxicity) and efficacy has so far prevented a major breakthrough. Synthetic, self assembling biomimetic polymer vesicles (BPVs) are a completely new technology with the advantage that they can be used as ideal targetting delivery systems. This study will help shed insight into whether BPVs are able to significantly better deliver treatment than conventional forms of therapy. Furthermore, because of the flexibility of BPV design and chemical makeup, this work will pave the way to develop targeted delivery agents to a whole range of other pathologic conditions. The project will provide the PDRA with detailed training in the use of mathematical modelling to understand and make predictions for biological systems. The project depends crucially on model development and refinement using experimental data, in collaboration with experimentalists. The resulting models will then be solved using analytical and numerical techniques, teaching a range of methods including perturbation theory, stability analysis and bifurcation theory and providing training in writing numerical codes and in efficient numerical simulation. The PDRA will benefit from the thriving research environments at Strathclyde and Sheffield. Strathclyde has active research programmes in Mathematical Biology (including research into neurological and cardiovascular disorders, blood cell morphology, epidemiology, marine science, medical devices and tissue bioengineering) and the regular seminars and workshops will enable the PDRA to interact with other senior researchers and thus gain a broad training in Mathematical Biology. Dr Craig Murdoch's (CM; see Section 4 of Description of Proposed Research) group has expertise in the bioengineering, chemistry, pathology and clinical aspects of tumour targetting. The consequent active, interdisciplinary research environment will be highly beneficial to the PDRAs career development. Additionally, the University of Strathclyde provides excellent training for PDRAs in the development of generic skills and competencies and thereby widen their scope for future employability. SDW's long term goal is to become a future leader in mathematical biology, with a focus on drug development. A key component of this progress is to establish a research group in mathematical biology which is at the forefront of developing models that can make quantitative, testable predictions about real patients. SDW is already supervising a PhD student on a project which is directly related to the proposal. The EPSRC first grant will provide the core support required to expand this group and make the most of the research opportunities of EPSRC's development programmes, including senior research fellowships and large programme grants. Furthermore, the proposed project involves a strong interaction with leading experimentalists ensuring that SDWs research lies at the forefront of the latest biological developments.

Publications

10 25 50
 
Description • Development of an analytically tractable statistical moment closure system describing the binding and uptake of ligand-coated nanoparticles into tumour cells.

• Development of a dynamic Monte Carlo model for nanoparticle uptake that predicts the critical effects of statistical variances in batch-to-batch variability on uptake.

• Development of a biomechanical model for nanoparticle uptake into avascular tumours that can be used to investigate infiltration patterns and treatment efficacy given different particle sizes and membrane properties.

• Theoretical predictions that explain differences in uptake between different cell lines and the critical dependency of uptake rate on cell receptor expression.

• Theoretical predictions to suggest that differences between cell endocytosis rates are unlikely to be responsible for the observed cell-to-cell differences in polymersome uptake.

• Theoretical predictions for co-cultures of multiple cell types that show the same polymersome uptake as cells cultured in isolation. This was confirmed by experimental studies.

• Polymersome uptake by cells in serum conditions was shown to be lower than uptake in serum free conditions.

• Development of a 3D in vivo computational model that will inform how to tune the surface chemistry of the BPVs to maximise the treatment efficacy.
Exploitation Route An increasing number of companies are exploring the use of nanotechnology for a wide range of medical applications, including drug and gene delivery, fluorescent labeling, diagnostic and imaging, anti-microbial techniques, bio-detection of pathogens, detection of proteins, probing of DNA structure, tissue engineering, phagokinetic studies and cell repair. Some techniques are currently in use while others are at various stages of testing and most of the major established companies have research programs on nanotechnology. The main problems for nanomaterials involve understanding possible toxic effects, how to improve their targeting and their controllability by external signals or by the local tissue environment. The research in this project is a first step towards constructing a modeling framework that can help reduce the risk and uncertainty in the particle-development process and provide guidance for the development of optimized nanomaterials for medical treatment. Our in vitro models are validated to reproduce data from concentration dependent experimental studies and accurately predict median number of polymersomes per cell and the percentage of cells that are positive for polymersomes. The validated models can provide insight into efficacy, safety and control of nanoparticle treatment. In particular, we can use the models to explain the differences in uptake between different cell lines, predict the optimal number of ligands per particle for maximal uptake, predict the critical effects of statistical variances in batch-to-batch variability on uptake, predict microenvironmental and cell-culture effects on uptake and inform dosage regimes and how to manipulate BPV properties to improve treatment targeting and delivery.
Sectors Healthcare,Pharmaceuticals and Medical Biotechnology

 
Description There are three papers currently in preparation to disseminate these key findings. The research described is nationally and internationally competitive. Much of the modelling work is of general interest to mathematicians working on multi-scale nonlinear spatially extended systems, as well as the mathematical biology and stochastic modeling communities. The results of our analysis are applicable to many pathologic conditions where nanoparticles are being used, and will provide the foundation for further work and collaboration. Of special interest is the analysis of the effects of nanoparticle size distribution, because of the increasing concern of batch-to-batch variability in particle production and particle-size effect on performance of nano treatment for real biomedical applications.
First Year Of Impact 2011
Sector Healthcare
Impact Types Societal

 
Description NC3Rs CRACK-IT Challenge 18 Targeting off-targets. Phase 1. Mathematical modelling guide receptor identification and toxicity prediction.
Amount £100,000 (GBP)
Organisation National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) 
Sector Public
Country United Kingdom
Start 01/2015 
End 07/2015
 
Description NC3Rs CRACK-IT Challenge 20 Metaboderm. Phase 1. Skin-in-a-box.
Amount £100,000 (GBP)
Organisation National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) 
Sector Public
Country United Kingdom
Start 01/2016 
End 07/2016
 
Description NC3Rs CRACK-IT Challenge 5 IVIVE. Development and mathematical modelling of Multicell-Bioreactors for in vitro to in vivo extrapolation of systemic chemical toxicity.
Amount £1,000,000 (GBP)
Funding ID NC/C011205/1 
Organisation National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) 
Sector Public
Country United Kingdom
Start 01/2013 
End 09/2016
 
Description NC3Rs Ph.D. studentship to study Modelling hepatic drug metabolism.
Amount £120,000 (GBP)
Organisation National Centre for the Replacement, Refinement and Reduction of Animals in Research (NC3Rs) 
Sector Public
Country United Kingdom
Start 10/2012 
End 10/2016
 
Title 3D tissue scale computational model 
Description A set of coupled PDEs is used to extrapolate information from the cell-scale BPV binding models (Objectives M.1 and M.2) to a 3D tissue-scale comprised of tumour vasculature and surrounding interstitium. Blood flow and oxygen delivery are modelled using an approach reported previously in the literature (Secomb, T. W., R. Hsu, et al. (2004). Green's function methods for analysis of oxygen delivery to tissue by microvascular networks. Annals of Biomedical Engineering 32(11): 1519-1529). An explicit 3D tumour network from a rat is used for the simulations, provided by our collaborator Prof. Tim Secomb (Department of Physiology, University of Arizona). The oxygen field is coupled to PDEs that describe the distribution of pH, BPVs and drug in the tumour mass. H+ ions are produced in low oxygen regions and able to diffuse; buffering effects are also accounted for. The simulated spatial distribution of the various agents is currently being validated against extensive histology information obtained from vascularised tumours embedded in dorsal skinfold chambers from Dr Craig Murdoch's lab (work being completed by SDW and RJS). The final model will inform both dosage regimes (the concentration of BPVs required to distribute a critical concentration of doxorubicin throughout the tumour mass), and how to tune the surface chemistry of the BPVs (binding and internalisation rates) to maximise the treatment efficacy. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact No impacts as yet 
 
Title Biomechanical model for avascular in vitro tumours 
Description The ligand-receptor binding kinetics model (Objective M.1) was incorporated into a biomechanical description of an in vitro avascular tumour spheriod. The computational model takes the form of multiphase partial differential equations assuming that the tumour consists of an inter-dispersed mixture of continuum phases (BPVs, tumour cells and extracellular fluid) coupled to a moving boundary representing the growing tumour surface. Both travellingwave and steadystate limits of the model are derived and studied and this allows us to make predictions about BPV infiltration patterns and treatment efficacy given different particle sizes and membrane properties. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact No impacts as yet 
 
Title Stochastic computational model for nanoparticle uptake into cancer cells 
Description We develop new mathematical descriptions of the ligand-receptor binding process (of BPVs to cancer cells). To do this we first derive a system of coupled differential equations describing the binding of BPV ligands to cell membrane receptors. To reduce the order of the system we apply novel statistical moment closure techniques to yield a much more amenable system (of equations for the mean number of bound BPVs per cell, the mean number of bonds per bound BPV and the associated standard deviations and higher order statistical moments). Closure is achieved by exploiting the fact that the distributions displayed typical Gaussian profiles, for which the higher moments can be calculated directly. A precise parameterization of this model is then achieved by converting this deterministic form into a stochastic model using a dynamic Monte Carlo Method and comparing the model simulations to the in vitro data. The parameterized framework can then be used to help fine tune the nanoparticle design (ligand number, particle size etc) for maximal uptake and treatment efficacy for different tumour conditions. 
Type Of Material Computer model/algorithm 
Provided To Others? No  
Impact No impacts as yet 
 
Description New collaborations 
Organisation University of Arizona
Country United States 
Sector Academic/University 
PI Contribution Additional collaborative links were made early in the project with Dr Helen Colley and Dr Vanessa Hearnden (Department of Clinical Dentistry, University of Sheffield). Both are experts in the generation of novel tissue engineered models of oral cancer to study invasion mechanisms and novel drug delivery and their expertise has been invaluable throughout the project in ensuring efficient encapsulation of the anti-cancer drugs into the polymersomes and obtaining subsequent uptake kinetics of the vesicles into the cancer cells, cultured as both monolayers (to provide data for model validation and parameterization in Objective M.1) and multi-cellular tumour spheroids (data for Objective M.2). Further, a new collaborative link was made through RJSs work with Prof. Tim Secomb (Department of Physiology, University of Arizona). Prof. Secomb provided two explicit tumour vascular structures as well as his Greens function solver, enabling a more accurate and physiologically-motivated picture of the therapeutic effect of BPVs in vivo to be established.
Collaborator Contribution Technical expertise and insight
Impact In Collaboration with RJS: 2012 NC3Rs CRACK-IT Challenge 5 IVIVE. Development and mathematical modelling of Multicell-Bioreactors for in vitro to in vivo extrapolation of systemic chemical toxicity. (P.I.) £1,000,000 2011 NC3Rs Ph.D. studentship to study Modelling hepatic drug metabolism. £120,000 In Collaboration with Dr Helen Colley: 2014 NC3Rs CRACK-IT Challenge 18 Targeting off-targets. Phase 1. Mathematical modelling guide receptor identification and toxicity prediction. £100,000 2016 NC3Rs CRACK-IT Challenge 20: Metaboderm. Phase 1: Skin-in-a-box. £100,000
Start Year 2011
 
Description American Association of Cancer Research Annual Meeting, Chicago, USA. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Poster presentation at a large international meeting with over 15K delegates. Some interesting discussions and questions were sparked with follow-up requests for information and collaboration.
Year(s) Of Engagement Activity 2012
 
Description Departmental seminar, School of Pharmacy and Biomolecular Sciences, LJMU. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Departmental seminar, School of Pharmacy and Biomolecular Sciences, LJMU. Was a good forum to kick-start new collaborations with colleagues in the Life Science Departments.
Year(s) Of Engagement Activity 2017
 
Description European Association for Cancer Research, Berlin. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Poster presentation at a large international meeting. Some interesting discussions and questions were sparked with follow-up requests for information and collaboration.
Year(s) Of Engagement Activity 2014
 
Description ICSB2013 International conference on systems biology. Copenhagen 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Poster presentation at a large international meeting. Some interesting discussions and questions were sparked with follow-up requests for information and collaboration.
Year(s) Of Engagement Activity 2013
 
Description Invited talk. Applied Mathematics Seminar. University of Birmingham. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 50 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2012
 
Description Invited talk. Applied Mathematics Seminar. University of Warwick. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 70 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2012
 
Description Invited talk. Biomechanical Engineering Seminar. University College London. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 15 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2013
 
Description Invited talk. Mathematical Biology Seminar. University of Bath. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 20 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2013
 
Description Invited talk. Mathematics and Computing Seminar. Stirling University. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 30 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2011
 
Description Invited talk. Maths-Bio-Medicine (MBM) Seminar. University of Leeds. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 40 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2011
 
Description Invited talk. School of Computing and Mathematics Seminar, University of Keele. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Other audiences
Results and Impact Departmental seminar in which around 10 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2015
 
Description Invited talk. School of Dentistry Seminar, University of Sheffield. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Departmental seminar in which around 30 people attended from undergraduates to full academic staff with a range of disciplinary backgrounds. The presentation sparked questions and discussion afterwards.
Year(s) Of Engagement Activity 2015